In the context of the recent increase in fuel cost, the importance of improved efficiency in axial-flow rotating machines has grown, such as industrial gas turbines and jet engines. One of means of improving efficiency in the axial-flow rotating machine is to reduce a blade loss. The blade loss is roughly classified into a profile loss occurring at a radial cross-sectional surface (airfoil) of a blade and the other losses. Examples of the other losses include a shock loss and a secondary loss. The recent axial-flow rotating machines subjected to a large load per one stage have an increased Mach number of working fluid flowing into a blade. Therefore, the shock loss tends to increase. In other words, a reduction in shock loss largely contributes to an improvement in performance of the rotating machine.
A technology (Water Atomization Cooling, WAC) has recently been studied in which fine droplets are sprayed to an air intake duct located at an inlet of a gas turbine compressor to cool intake air through the evaporation thereof for performance improvement. Incidentally, the technology relating to the WAC is described in e.g. patent document 1. The WAC is executed to lower the inlet temperature of the compressor; therefore, the overall gas turbine tends to increase a pressure ratio. Further, the evaporation resulting from the WAC causes a mixture gas of main flow air and water vapor. Since this mixture gas has lower acoustic velocity than air due to the presence of mixed water vapor, the Mach number increase which is the ratio of flow velocity to acoustic velocity. Thus, it is expected that shock loss at a transonic stage will increase.
Studies to reduce a shock loss have been made in the past. One of them is a study in which the shape of a stacking line is modified, with the stacking line being a line connecting together the gravity center positions of airfoil at respective spanwise positions. As shown in patent document 2, the following blade is proposed as a technology for modifying the shape of the stacking line. The cross-sectional surfaces in a range from a mean cross-sectional surface, which is an intermediate cross-sectional surface between a hub cross-sectional surface and a tip cross-sectional surface, to the hub cross-sectional surface and the tip cross-sectional surface are shifted toward the upstream side to form an S-shaped stacking line. In addition, the amount of shifting of the tip cross-sectional surface is maximized. Patent document 2 teaches that shifting the tip side toward the upstream can reduce various losses caused by shock waves. If the tip side is shifted toward the upstream side, there is a problem as below. A flow is earlier increased in velocity on the tip side to lower static pressure. A flow on the hub side moves toward the tip side to reduce the flow rate, which makes it easy to develop a boundary layer on the hub side. In patent document 2, the amount of downstream shift of the blade cross-sectional surfaces close to the mean cross-sectional surface is reduced, thereby suppressing an increase in loss resulting from the development of the boundary layer on the hub side.